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CN105469439B - Using the SLM micro-vision data reconstruction methods of residual feedback - Google Patents

Using the SLM micro-vision data reconstruction methods of residual feedback Download PDF

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CN105469439B
CN105469439B CN201510849940.2A CN201510849940A CN105469439B CN 105469439 B CN105469439 B CN 105469439B CN 201510849940 A CN201510849940 A CN 201510849940A CN 105469439 B CN105469439 B CN 105469439B
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王跃宗
王军帅
赵志忠
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Beijing University of Technology
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Abstract

The present invention relates to the SLM micro-vision data reconstruction methods using residual feedback, made improvements more particularly to based on pinhole camera modeling by carrying out residual analysis to lift the method for SLM micro-vision system reconstruction accuracies.This method mainly includes the following steps that:Equidistantly collection SLM stereo pairs, image alignment and parallax distortion correction, establish initial visual model, and reconstructed residual calculates, reconstructed residual accuracy evaluation, residual compensation.The present invention is on the basis of pinhole camera modeling advantage is retained, by establishing residual compensation model, SLM vision systems a variety of errors present in reconstruct data procedures are compensated, reduce parameter calibration difficulty, when overcoming the shortcomings of that existing pin-hole model is applied in low-light field, new model has stronger practicality.For any one SLM vision system, as long as being determined that residual compensation model can exports high-precision reconstruct data.

Description

Using the SLM micro-vision data reconstruction methods of residual feedback
Technical field:
The present invention relates to a kind of SLM micro-vision data reconstruction methods using residual feedback, more particularly to pin hole Made improvements based on camera model by establishing residual compensation model to lift SLM micro-vision system reconstruction accuracies Method.
Background technology:
Optics Stereo microscope is a kind of accurate optical instrument, is broadly divided into CMO types SLM (stereo light System), Greenough types SLM.CMO types SLM two cover light paths share the big object lens in front end, altogether comprising three optical axises, and It is parallel to each other.CCD camera is installed at CMO types SLM sub-light road image planes and may make up SLM microscopic stereovision systems, SLM is micro- Vision system belongs to typical computer Binocular Stereo Vision System, possesses larger working space, and belongs to contactless Optical measurement, by camera can captured in real-time object space whole scene, be delayed in the absence of the signal of similar electron microscope, this A little features make it gradually be widely used in the fields such as microoperation, micrometering amount, micro assemby.Small items are carried out with microoperation, it is micro- Measurement need to carry out accurate reconstruction to its three-dimensional object space, and the visual modeling of efficiently and accurately is the key point being operated.
Visual modeling is one of the important research content of SLM micro-vision systems during progress microoperation, micrometering amount. Pin-hole model is linear model, the extensive use in macroscopical stereoscopic vision, is a kind of ripe easy vision mode, but simultaneously uncomfortable Close the reconstruct for being directly used in SLM micro-vision coordinates.Because CMO-styleSLM imaging process does not meet the original of pin-hole imaging Reason, larger position error can be produced when directly carrying out three-dimensionalreconstruction using pin hole camera model.Error hiding is easily caused, is grasped by mistake Make, reduce micrometering amount, microoperation, micro assemby, during operating efficiency.Kim (1990) has used easy vision mode, than Earlier the SLM micro-vision systems of quantization be applied to microcosmos measurement in, highly significant, but model used it is less Parameter it is weaker to lens distortion resistivity.Danuser (1999) establishes a high-precision vision mode, comparison system The calibration process for discussing parameter, it is very representative, but model introduces substantial amounts of parameter to be fitted distortion, it is necessary to design multiple Miscellaneous calibration process estimation parameter, if selected for inappropriate optimization process, the introducing of quantity of parameters frequently can lead to demarcate As a result unstability, the model that Danuser (1999) is proposed use relatively difficult.
The content of the invention
Complicated for above-mentioned reconstructing method calibration process, precision is low, directly using pin-hole model in SLM micro-vision systems In by image coordinate reconstruct object space world coordinates when existing larger position error problem, the present invention is proposed anti-using residual error The SLM micro-vision data reconstruction methods of feedback, the purpose is on the basis of pin-hole model advantage is retained, it is difficult to reduce parameter calibration Degree, by establishing residual compensation method, when overcoming the shortcomings of that existing pin-hole model is applied in low-light field, improve micro-structural 3 D Topographic data reconstruction accuracy, new method have stronger practicality.
SLM micro-vision data reconstruction methods using residual feedback involved in the present invention, are built upon pin hole and take the photograph phase On machine model, the residual error that data are reconstructed to SLM micro-visions carries out analysis compensation.Described method comprises the following steps:
1st, SLM stereo pairs are equidistantly gathered
By SLM micro-vision systems in world coordinate system along x-axis, y-axis, z-axis equidistantly gathers stereo pairs, defeated Go out x-axis image sequence, y-axis image sequence, z-axis image sequence.Obtain image lattice point world coordinates truth set P1
2nd, image alignment and parallax distortion correction
In x-axis image sequence, using fitting algorithm, respectively to collected left image, characteristics of image in right image Point travel track is fitted, and estimates left images relative rotation angle and relative skew, carries out left images alignment, correction left and right Image parallactic curved surface distorts.
3rd, initial visual model is established
It is theoretical by pinhole camera modeling using calibration software, initial alignment, output demarcation are carried out to SLM vision systems Parameter.Using the image sequence collected along z-axis, left and right stereo pairs parallax data is counted, establishes parallax increment With z-axis increment of coordinate linear relationship, parallax increment proportionality coefficient E is exported, provides initial vision mode.
4th, reconstructed residual calculates
Equidistantly during collection image sequence, when image is moved to position 2 by position 1, all lattice points have identical movement Distance D1.X-axis image sequence is reconstructed using initial model, y-axis image sequence, the world coordinates of z-axis image sequence lattice point, is obtained The set of measurements P of all lattice point world coordinates2, calculate the relative reconstruction distance D that lattice point is moved to position 2 by position 12.With D1 As true value, D2As measured value, relative displacement residual error parameter reconstruct lattice point is calculated.Relative displacement residual error parameter bag Along x-axis axial dipole field residual error when including reconstruct x-axis image sequence, along y-axis radial deflection residual error, along z-axis radial deflection residual error;Reconstruct During y-axis image sequence, along y-axis axial dipole field residual error, along x-axis radial deflection residual error, along z-axis radial deflection residual error;Reconstruct z-axis figure During as sequence, along z-axis axial dipole field residual error, along x-axis radial deflection residual error, along y-axis radial deflection residual error.
5th, reconstructed residual accuracy evaluation
According to SLM micro-vision system data reconstruction required precisions, residual error section is selected, to ensure higher reconstruction accuracy, Residual error section can be chosen in the range of from (- 5 μm, 5 μm) to (- 200 μm, 200 μm).The smaller then reconstruct essence of residual error interval range Degree is higher, is determined according to user.The quantity K of residual sample point of the statistics in the section, participate in total residual sample of statistics Point quantity is designated as U, defines effective ratio coefficient S=K/U.When residual error section, setting is smaller, and S is bigger, illustrates that reconstruction accuracy is higher, Residual error data divergence is smaller.Remember that reconstructed residual accuracy evaluation parameter is M.According to the value of effective ratio coefficient S to reconstructed residual Precision is assessed.Work as S<During M, it is believed that reconstruction accuracy is low, need to carry out residual compensation.Work as S>During M, it is believed that reconstruction accuracy meets will Ask.To obtain higher reconstruction accuracy, selected reconstructed residual accuracy evaluation parameter M value should be greater than being equal to 0.85.
6th, residual compensation
Reconstruct residual precision low parameter is compensated respectively using linear compensation method.On the basis of initial model, first During to reconstruct x-axis image sequence, reconstructed residual precision low parameter carries out linear compensation, exports compensating parameter, obtains mending for the first time Chang Hou worlds coordinate vector.Reconstructed residual precision low parameter is linearly mended when on this basis, to reconstruct z-axis image sequence Repay, export compensating parameter, obtain world's coordinate vector after second of compensation.When finally to reconstruct y-axis image sequence, reconstructed residual Precision low parameter carries out linear compensation, exports compensating parameter, exports High precision reconstruction data.
SLM micro-vision data reconstruction methods using residual feedback involved in the present invention, first, it is abnormal to establish parallax Become the method for correction, the Various types of data of needs is obtained from demarcation template image, the methods of using linear fit, fitting of a polynomial Correcting parallax distorts;Then, the reconstructing method of z coordinate is corrected in conventional pinhole camera model theoretical foundation, is established initial Vision mode;Finally, error compensation is carried out to initial visual model, establishes residual compensation model, export high-precision reconstruct Data.Reconstructed error in the microoperation based on SLM micro-vision systems, microassembly system comes from many factors, such as The defects of vision mode itself, lens distortion, the positioning precision etc. of drive component, the residual error for reconstructing data is the comprehensive of all errors Zoarium, residual compensation model are fitted to the residual error for reconstructing data, compensate reconstructed error.This modeling method has stronger Adaptability, for any one SLM vision system, as long as being determined that residual compensation model can exports high-precision reconstruct Data.
Accompanying drawing is as follows
Fig. 1 is the SLM micro-vision data reconstruction method flow charts of the present invention using residual feedback
Fig. 2 is image of the present invention alignment and the flow chart of parallax distortion correction method
Fig. 3 is the flow chart of the present invention for establishing initial visual model
Fig. 4 is residual compensation flow chart of the present invention
Fig. 5 is the residual error data distribution map after the SLM micro-visions data reconstruction method reconstruct using residual feedback
Fig. 6 is the residual error data distribution map of the present invention using pin-hole model reconstructing method
Embodiment:
The present invention is further elaborated in conjunction with accompanying drawing.Fig. 1 shows of the present invention using residual feedback SLM micro-vision data reconstruction method flow charts, as illustrated, the SLM micro-vision data reconstruction methods using residual feedback Comprise the following steps:
1st, SLM stereo pairs are equidistantly gathered
Latticed plane reference model is made by MEMS technology, demarcates on model and designs the row circular pattern of 7 rows × 7, directly Footpath is 0.15mm, and contiguous tokens pattern circle spacing is 0.3mm, and the positioning precision of array lattice point is ± 0.25 μm, circular pattern Central point be defined as lattice point.Demarcation model is fixed on the drive means, focusing surface of the IMAQ plane generally within SLM Place, SLM has effective depth scope, and centered on focusing surface, the effective depth scope for using SLM is about ± 1.13mm.
Demarcation model equidistantly moves along world coordinate system x-axis, y-axis, z-axis respectively, is set to 0.1mm and passes through SLM Micro-vision system equidistantly gathers demarcation model stereo pairs S11, and the acquisition length scope of x-axis, y-axis and z-axis is respectively 4.1mm, 2.9mm and 3.1mm, export x-axis image sequence S21, y-axis image sequence S22, z-axis image sequence S23.Obtain image Lattice point world coordinates truth set S31, is designated as P1(xw1,yw1,zw1)。
2nd, image alignment and parallax distortion correction
(1) critical function of SLM micro-visions is the depth using disparity estimation object space, i.e. world coordinate system Longitudinal coordinate, in order to establish the higher vision mode of the linearity, image alignment and parallax distortion correction S41 need to be carried out.Input x-axis Image sequence S21, the running orbit of lattice point in the picture are approximately straight line, x-axis direction of the traffic direction along image, but and x-axis It is and not parallel.Using fitting algorithm such as:Least square method, respectively left image, each image pane in right image to being collected Point travel track is fitted S24, and fitting a straight line set of slopes k is obtained by left image sequencel, each fitting a straight line is with respect to x-axis rotation Corner is αl=arctankl, fitting a straight line set of slopes k is obtained by right image sequencer, each fitting a straight line is with respect to the x-axis anglec of rotation For αr=arctankr.Make αlWith αrMake difference and be averaged α, as left images relative rotation angle.Using left image as base Standard, right image coordinate rotation-α angles, realizes and is corrected S25 to rotating against to sequence of left-right images.Output image lattice point is sat Mark S26.Note rotation rear left image sequence lattice point image coordinate collection is combined into (xl,yl), right image sequence lattice point image coordinate collection is combined into (xr,yr)。
(2) input picture lattice point coordinate S26, inputs y-axis image sequence S22, and input z-axis image sequence S23 estimates jointly The relative offset distance T of left images in the vertical direction.Make the vertical seat of left images corresponding lattice point image in each image sequence Mark ylWith yrIt is poor to make, and is averaged after all difference summations, the as longitudinally opposed offset distance T of left images.Using left image as base Standard, right image translate T in y-axis direction, realize that skew longitudinally opposed to left images is corrected.By relative to left images Rotation is corrected with skew realizes that left images are directed at S32.Export aligned rear lattice point image coordinate (x2,y2).Left image sequence Row lattice point image coordinate is designated as (x2l,y2l), right image sequence lattice point image coordinate is designated as (x2r,y2r)。
(3) in SLM vision systems, parallax is the important technology index for reconstructing z coordinate in world coordinate system, need to use warp The x-axis image sequence of image alignment is corrected to the distortion of left images parallax.Lattice point initial parallax P is by formula P=y2r-y2l It is calculated, in x-axis image sequence, the corresponding parallax geometric locus of a lattice point, uses fitting a straight line lattice point abscissa x2With parallax P corresponding relations, fitting parallax straight line S33.Export parallax linear equation:Y=Kpx2+ B, K in formulapTo be fitted parallax Straight slope set, B are intercept set, and Y is fitting parallax value.Fitting a straight line residual error N is calculated, formula is:N=Y-P.Utilize plan Hop algorithm is such as:Least square method, regression criterion N and lattice point abscissa x2Polynomial relation, fitting second order formula are:N1=A (x2 )2+B(x2)2+C.Obtain parallax correction formula P0=P-N1.It is final to realize to image sequence alignment and parallax distortion correction.Output Lattice point image coordinate vector S36.
3rd, initial visual model is established
Lattice point image coordinate vector S36 is inputted, it is theoretical according to pinhole camera modeling, establish and sat by image coordinate to the world Mark the initial visual model S51 of conversion.Using camera calibration software such as:Halcon, to joining inside monochromatic light road in SLM vision systems Number a, the external parameter b of the relatively left camera of right camera, left camera is estimated with respect to the pose parameter c of world coordinate system, exports Model parameter S52.Using along z-axis image sequence S23, multigroup stereo pairs can be obtained.With the lattice of first group of stereo pairs On the basis of point parallax, the parallax increment of each group of stereo image pair lattice point is calculated, parallax incremental data is counted, established Parallax increment ratio coefficient S 54, is designated as E.Using fitting algorithm such as:Least square method, fitting stereo pairs lattice point parallax P0 With z coordinate increment linear relationship S53, i.e. z=E × P0, E is parallax increment proportionality coefficient, and representative image parallax changes 1 pixel The increment of corresponding z coordinate.Export the initial visual model after improving to Z coordinate reconstruction accuracy.Output is through initial visual The image sequence lattice point world coordinates vector S61 of model reconstruction.
4th, reconstructed residual calculates
Equidistantly during collection image sequence, image sequence lattice point has real world coordinates set P1(xw1,yw1,zw1), mark When random sample plate is moved to collection position 2 by gathering position 1, demarcating 49 lattice points on model has same displacement D1.In x-axis image Sequence, y-axis image sequence, using first IMAQ point as reference position on z-axis image sequence, be defined on it is all remaining 49 lattice point world coordinates are combined into respect to the world coordinates relative displacement collection of first image capture position lattice point when gathering position G1.When reconstructing x-axis image sequence using initial model, y-axis image sequence, the world coordinates of z-axis image sequence lattice point, institute is obtained There is the reconstruct value set S55 of lattice point world coordinates, be designated as P2(xw2,yw2,zw2), calculate lattice point on demarcation model and moved by position 1 To the relative reconstruction displacement D of position 22, 49 lattice point relative reconstruction displacement D2It is and unequal.Using first IMAQ point as Reference position, 49 lattice point reconstruct with respect to first image capture position lattice of world coordinates when being defined on remaining all collection position The reconstruct world coordinates relative displacement collection of point is combined into G2
With G1As true value, G2As measured value, G is made1With G2It is poor to make, and calculates respectively in world coordinate system along between x-axis etc. During away from collection image, relative displacement residual error parameter E between lattice point is reconstructedX.Along x-axis axial dipole field during including reconstruct x-axis image sequence Residual error EXX, along y-axis radial deflection residual error EXY, along z-axis radial deflection residual error EXZ.When equidistantly gathering image along y-axis, lattice are reconstructed Relative displacement residual error parameter E between pointY, including along y-axis axial dipole field residual error EYY, along x-axis radial deflection residual error EYX, along z-axis radially Offset residual error EYZ.When equidistantly gathering image along z-axis, relative displacement residual error parameter E between lattice point is reconstructedZ, including it is axially inclined along z-axis Move residual error EZZ, along x-axis radial deflection residual error EZX, along y-axis radial deflection residual error EZY.Join comprising nine relative displacement residual errors altogether Number.
5th, reconstructed residual accuracy evaluation
Assessment S81 is carried out to reconstruct residual precision, given residual error section (- 10 μm, 10 μm), in x-axis image sequence, y-axis Image sequence, relative skew residual error parameter E is counted in z-axis image sequenceXX, EXY,EXZ,EYY, EYX,EYZ, EZZ, EZX, EZYPositioned at this The quantity K of residual sample point in section, the total residual sample point quantity for participating in statistics are designated as U, define effective ratio coefficient S =K/U, when residual error section, setting is smaller, and S is bigger, illustrates that reconstruction accuracy is higher, and residual error data divergence is smaller.Remember reconstructed residual Accuracy evaluation parameter is M.Reconstruct residual precision is assessed according to the value of effective ratio coefficient S.To ensure reconstruction accuracy, take M=0.95.Work as S<During M, it is believed that reconstruction accuracy is low, need to carry out residual compensation.Work as S>During M, it is believed that reconstruction accuracy meets to require.It is right When reconstruction accuracy is unsatisfactory for requiring, residual compensation need to be carried out.E is found after carrying out residual precision assessmentXX, EYY, EYX, EZX, EZY Five parameter reconstruction accuracies are low, need to carry out residual compensation S91.
6th, residual compensation
E is corrected using linear compensation method respectivelyXX, EYY, EYX, EZX, EZY.On the basis of initial model, first to x, y-axis axle To reconstructed residual EXX, EYYTwo parameters carry out linear compensation S92, formula xw3=xw2(1+KX), yw3=yw2(1+KY), export x Axle nose balance COEFFICIENT KX, export y-axis nose balance COEFFICIENT KY, obtain world coordinate vector (x after compensating for the first timew3,yw3, zw3).On this basis, to z-axis radial direction reconstructed residual EZX, EZYCarry out linear compensation S94, formula xw4=xw3+(KXZ·zw3), yw4=yw3+(KYZ·zw3).Export z-axis radial compensation COEFFICIENT KXZ, KYZ, obtain world coordinate vector (x after second of compensationw4, yw4,zw4).The finally radial direction residual error E to relative displacement on y-axis image sequence along the x-axis directionYXCarry out linear compensation S96, formula For xw5=xw4+(KXY·yw4), output penalty coefficient KXY, world coordinate vector (x after output third time compensatesw5,yw5,zw5).It is defeated Go out High precision reconstruction data S101.
In order to illustrate High precision reconstruction ability of this method in SLM micro-vision systems, we use Halcon softwares The demarcation of the pinhole camera modeling of offer, reconstructed module are calculated in x-axis image sequence, y-axis image sequence and z-axis image sequence The world coordinates of lattice point, count the residual error data of pin-hole model reconstruction result, and the residual error number after being reconstructed with context of methods According to being compared.As illustrated, Fig. 5 is the residual error data distribution map after being reconstructed using this method.Δ X in diagramX,AFor x-axis figure As the collection distance of sequence, Δ YY,AFor the collection distance of y-axis image sequence, Δ ZZ,AFor the collection distance of z-axis image sequence.From It can be seen from the figure that, EXX, EXY,EXZ,EYY, EYX,EYZ, EZX, EZYData distribution in residual error section (- 10 μm, 10 μm), have Proportionality coefficient S values are imitated more than 95%, fully meet reconstruction accuracy requirement.In SLM effective depths scope ± 1.13mm, that is, work as |ΔZZ,A|<When 2.26, EZZEffective ratio coefficient S value of the data in residual error section (- 10 μm, 10 μm) be 96.4%, can Meet the requirement of Z coordinate reconstruction accuracy.
Fig. 6 is the residual error data distribution map using pin-hole model reconstructing method, it can be seen that its EXX、EXY's Data distribution is in (- 10 μm, 10 μm) section, EXZData scatter degree it is larger, maximum residul difference is close to 0.15mm.|EYX|、|EYY |、|EZX|、|EZY| and | EZZ| maximum respectively close to 0.04mm, 0.08mm, 0.1mm, 0.2mm, 0.2mm, EYZData master It is distributed in ± 0.02mm residual error section.Fig. 6 illustrates the reconstruction accuracy of pinhole camera modeling well below present invention side The reconstruction accuracy of method, the inventive method have stronger adaptability, higher reconstruction accuracy ability, for any one SLM Vision system, as long as being determined that residual compensation model can exports high-precision reconstruct data.

Claims (3)

1. using the SLM micro-vision data reconstruction methods of residual feedback, it is characterised by comprising the following steps:Equidistantly collection SLM stereo pairs, image alignment and parallax distortion correction, establish initial visual model, and reconstructed residual calculates, reconstructed residual essence Degree is assessed, residual compensation;Equidistantly collection SLM stereo pairs are specially:By SLM micro-vision systems in world coordinate system It is middle equidistantly to gather stereo pairs along x-axis, y-axis, z-axis, export x-axis image sequence, y-axis image sequence, z-axis image sequence; Obtain image lattice point world coordinates truth set P1
Image is aligned with parallax distortion correction:In x-axis image sequence, using fitting algorithm, respectively to being collected Left image, image characteristic point travel track is fitted in right image, estimate left images relative rotation angle and relative skew, Carry out left images alignment, the curved surface distortion of correction left images parallax;
Establishing initial visual model is specially:It is theoretical by pinhole camera modeling using calibration software, SLM vision systems are entered Row initial alignment, export calibrating parameters;Using the image sequence collected along z-axis, left and right stereo pairs parallax data is entered Row statistics, establishes parallax increment and z-axis increment of coordinate linear relationship, exports parallax increment proportionality coefficient E, provides initial vision Model;
Reconstructed residual calculates:Equidistantly during collection image sequence, when image is moved to position 2 by position 1, all lattice points With identical displacement D1;X-axis image sequence, y-axis image sequence, z-axis image sequence lattice point are reconstructed using initial model World coordinates, obtain the set of measurements P of all lattice point world coordinates2, calculate the phase that lattice point is moved to position 2 by position 1 To restructuring distance D2;With D1As true value, D2As measured value, relative displacement residual error parameter reconstruct lattice point is calculated;It is residual Along x-axis axial dipole field residual error when difference includes reconstructing x-axis image sequence, along y-axis radial deflection residual error, along z-axis radial deflection residual error; When reconstructing y-axis image sequence, along y-axis axial dipole field residual error, along x-axis radial deflection residual error, along z-axis radial deflection residual error;Reconstruct z During axle image sequence, along z-axis axial dipole field residual error, along x-axis radial deflection residual error, along y-axis radial deflection residual error.
2. the SLM micro-vision data reconstruction methods according to claim 1 using residual feedback, it is characterised in that weight Structure residual precision is assessed:Chosen in the range of residual error section from (- 5 μm, 5 μm) to (- 200 μm, 200 μm);Statistics The quantity K of residual sample point in the section, the total residual sample point quantity for participating in statistics are designated as U, define effective ratio Example coefficient S=K/U;When residual error section, setting is smaller, and S is bigger, illustrates that reconstruction accuracy is higher, and residual error data divergence is smaller;Note Reconstructed residual accuracy evaluation parameter is M;Reconstruct residual precision is assessed according to the value of effective ratio coefficient S;Work as S<During M, Think that reconstruction accuracy is low, residual compensation need to be carried out;Work as S>During M, it is believed that reconstruction accuracy meets to require;To obtain higher reconstruct essence Degree, selected reconstructed residual accuracy evaluation parameter M value should be greater than being equal to 0.85.
3. the SLM micro-vision data reconstruction methods according to claim 1 using residual feedback, it is characterised in that residual Difference compensates:Reconstruct residual precision low parameter is compensated respectively using linear compensation method;On the basis of initial model, When first to reconstruct x-axis image sequence, reconstructed residual precision low parameter carries out linear compensation, exports compensating parameter, obtains first World's coordinate vector after secondary compensation;Reconstructed residual precision low parameter is carried out linear when on this basis, to reconstruct z-axis image sequence Compensation, compensating parameter is exported, obtains world's coordinate vector after second of compensation;When finally to reconstruct y-axis image sequence, reconstruct is residual Poor precision low parameter carries out linear compensation, exports compensating parameter, exports High precision reconstruction data.
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